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\frac{1}{2}+\frac{1}{3}
Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.
\frac{3}{6}+\frac{2}{6}
Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.
\frac{3+2}{6}
Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.
\frac{5}{6}
Add 3 and 2 to get 5.